ITV1’s new current affairs strand, Exposure, had an almost terminally embarrassing start last year, when footage of a video game was accidentally used in its first programme instead of real footage of IRA violence. Last night, Exposure proved conclusively that it deserved to survive that initial snafu, with its excellent exposé The Other Side of Jimmy Savile.

This was populist current affairs at its very best. Like many top-notch TV investigations, it has caused significant ripples in the days before its transmission – notably the BBC launching an investigation into Savile’s behaviour while he was at the corporation.

But unlike many other documentaries, this edition of Exposure was also a gripping watch from start to finish.

Its presenter, Mark Williams-Thomas, is a former police detective, specialising in child protection. In an investigation lasting nearly a year, he has found women who were willing to speak about alleged abuse at the hands of Savile, as well as independent witnesses who gave testimony about Savile’s behaviour.

Sue Thompson, who worked for the BBC in Savile’s home city of Leeds in 1978, told of opening his dressing room door to find Savile with a girl, who looked about 14, on his knee. “It was his tongue, that was just sort of coming out of her mouth, that stuck in my mind,” said Thompson.

There was also direct testimony of alleged sexual abuse by Savile, from two women who are former pupils at Duncroft Approved School in Surrey. Charlotte said that, when she was 14, Savile had put his hand up her jumper. And when she screamed and complained, she was sent to the school’s isolation unit – effectively a padded cell. Fiona said that Savile had gone further with her, having “a good fumble around in my knickers”.

Of course, Savile is now dead, and cannot put his side of the story in response to any of these allegations. But Williams-Thomas’s case against Savile convinced a QC, Ian Glen, that there enough evidence for Savile to be arrested if he were still alive. Glen’s contribution made the programme feel even more authoritative.

At the end of the programme, Williams-Thomas showed his evidence – including the women’s on-camera interviews – to Esther Rantzen. At first, it seemed odd to include Rantzen, given that – unlike the programme’s other interviewees – she offered no direct evidence of inappropriate behaviour by Savile.

But as she spoke, her contribution became hugely compelling. “I’m afraid the jury isn’t out any more,” said Rantzen, fighting back tears. “We all blocked our ears to the gossip – there was gossip, and there were rumours.”

And that was the thread that made this programme so very chilling. I grew up in Leeds, and when I was a kid there were lurid playground rumours about Savile, which went far beyond suggestions of abuse of teenage girls. Last night’s programme not only got to the heart of direct allegations against Savile, but vividly posed the question: why was nothing ever done, when the rumours were so persistent?

That question took what might otherwise have been a salacious celebrity scandal and turned it – like last week’s case in Rochdale – into serious questions about institutional failure. It’s hard to imagine current affairs on ITV ever being stronger.